I was hoping to get a reference particularly for the $ \Leftarrow $ half of the equiconsistency $$\operatorname{Con}(\mathrm{ZFC} + \text{“There are infinitely many Woodin cardinals"}) \iff \operatorname{Con}\left(\mathrm{ZFC} + \mathrm{AD}^{L(R)}\right)\text.$$
2026-03-30 05:31:55.1774848715
Reference for consistency strength of ZFC + AD$^{L(R)}$
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The reference you want is
Other sources (such as the final chapter of Kanamori's book) briefly discuss the result, but this is the only place where the details are given. More recent papers deal with extensions, but they all build on this work. The result is due to Woodin, the history is described carefully in the chapter.